The human papillomavirus (HPV) can cause a number of cancers, including cervical and throat cancers. The National Cancer Institute (NCI) Surgery Branch has developed an experimental therapy that involves taking white blood cells from patients' tumors, growing them in the laboratory in large numbers, and then giving the cells back to the patient. These cells are called Tumor Infiltrating Lymphocytes, or TIL and we have given this type of treatment to over 200 patients with melanoma. Researchers want to know if TIL shrink s tumors in people with human papilloma virus (HPV)-related cancer. In this study, we are selecting a specific subset of white blood cells from the tumor that we think are the most effective in fighting tumors and will use only these cells in making the tumor fighting cells.